In this lesson you’ll learn the concepts and basics of Classification of Triangles
and how to use the properties of particular type for applications. The related
contents, explanation with examples are presented by instructor using video and
in own hand writing. This will provide the geometry help; in context with triangles
and applying the developed skills, for finding solution to real-world problems.
The two common systems and basis of triangle classifications are: first by their
sides and the second by their angles. For a triangle, you can have all the
three sides congruent (equal measure), or two sides congruent, or no side
congruent.Congruent sides and congruent angles of triangles are often marked
as in the following figures:
(More text below video...)
Scalene triangle: In a scalene triangle
ABC, all the
three sides and angles are different from one another
(see the figure below).
Isosceles triangles: An isosceles triangle has two sides equal in length,
called legs or lateral sides and the third side is known as base.
In an isosceles triangle, the angles opposite the equal sides also measure equal. In the above isosceles ABC, the side AB=AC and ABC =ACB, so
ABC is classified as an Isosceles triangle. Equilateral triangle: In an equilateral triangle, all the sides have the same length. This means that the
angles are also equal and hence this form of triangle is also called an equiangular triangle.
You know from earlier learning that the sum of the interior angles of any triangle must equal to
180,
therefore, each angle of an equilateral triangle shall be
60.
In the above equilateral ABC,
the sides AB = BC = CA and
ABC
= BCA
= CAB =
60.
Classification by angles:
Acute Triangle: In an acute triangle all the three angles measure less than 90 degrees.
E.g. in ABC,
all the three i.e. A,
C and
B
are acute angle (Fig- 4).
Right Triangle: In a right triangle, there is one right angle, which measures
90.
This implies that the other two angles will be necessarily acute.
In Fig-5 below, the right angle square has been shown and marked as M to show a right angle.
Obtuse Triangle: In an obtuse triangle, one internal angle measures more than
90.
It also implies; other two angles will be acute.
In ABC,
measure of
CBA
is more than
90. (Fig- 6 below).
For example, Given: the below triangle, where sides AC=AB and
ABC
= 65
and ACB
= 65.
Classify this triangle and find out measure of angle
BAC.
You know that the summation of three angles of a triangle equals to
180.
Then
BAC
= [180
- (65
+ 65)]
= 50.
As both the sides AC = AB, so then
ABC is an Isosceles triangle.
mBAC =
50
and the triangle is an Isosceles triangle, is the final answer.
Remember -triangle classification: scalene triangle, isosceles triangle, equilateral
triangle acute-angled triangle, obtuse-angled triangle. right-angled triangle.
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ABC, all the
three sides and angles are different from one another
(see the figure below).
ABC =
,
therefore, each angle of an equilateral triangle shall be
60
